Modeling and Optimal Design of Photonic Structures

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NSF Award Abstract - DMS-0072439Mathematical Sciences: Modeling and Optimal Design of Photonic StructuresAbstract0072439 DobsonThis project focuses on the investigation and development of new computational methods and analytical techniques for the modeling and optimal design of photonic crystals and related structures. The objectives of the project are to extend methods developed for two-dimensional photonic crystals to the case of three-dimensional structures, to develop methods for the optimization of defect modes in photonic band gap structures, and to model and analyze the effects of dispersive media on wave propagation in periodic structures and study associated optimal design problems. The final objective is to model truncated photonic crystals in planar geometries and develop methods to optimize the scattering and resonance properties of such structures. The structures studied in this project are periodic arrangements of optical materials, designed to exhibit useful properties with respect to electromagnetic wave propagation. Making use of such structures is a fundamental technology, expected to have a significant impact in applications including lasers, sensors, optical storage, optical communications, and high-density optical interconnects. This project aims to develop modeling and design capabilities, which will improve understanding of the properties of these structures and facilitate their incorporation into useful devices.